Problem: What's the first wrong statement in the proof below that $ \triangle DEB \cong \triangle CEB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{CF} \cong \overline{BD}$ $, \ $ $ \angle CFE \cong \angle DBE$ $, \ $ $ \overline{EF} \cong \overline{BE}$ $, \ $ $ \overline{AB} \cong \overline{BE}$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ and $\ $ $ \angle ACB \cong \angle BDE$ Proof $ \triangle DEB \cong \triangle CEF$ because SAS $ \angle BED \cong \angle BEC$ because alternate interior angles are equal $ \overline{DE} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \triangle CEB \cong \triangle DEB$ because SAS $ \triangle DEB \cong \triangle CAB$ because AAS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle BEC \cong \angle BED$ is the first wrong statement.